Chapter IV: Effective Lewis numbers in turbulent non-premixed flames
4.2 Review of experimental data
terized, and a deeper understanding is needed. It is the objective of this chapter to perform an analysis similar to the work of Savard & Blanquart [47] for turbu- lent non-premixed flames. More precisely, the present work has three goals: (i) to propose a flamelet-based methodology to extract effective Lewis numbers from data sets of turbulent diffusion flames, (ii) to apply the proposed methodology to the Sandia piloted CH4/air flames [72], and (iii) to assess the validity of previously- suggested models forγ based on relevant turbulence/flame parameters. This anal- ysis is carried out using the well-documented experimental database of Barlowet al.[72].
This chapter is organized as follows: Sec.4.2provides an overview of the experi- mental data that is used in this work. Section4.3 outlines the procedure to extract effective Lewis numbers from the experimental data. Section 4.4 provides a dis- cussion of potential biases to the present analysis. In Sec.4.5, a k-εmodel used in other studies to model γ, is applied to the present analysis. Section4.6 presents a discussion of additional modeling attempts for γ, based on the Karlovitz number.
Finally, a summary of the observations is provided in Sec.4.7.
4.2 Review of experimental data
The data considered for this work is composed of four of the six Sandia non- premixed methane/air jet flames, made available from the TNF workshop [72]. The same burner [126, 127] is used for all jet flames, which differ only by their jet Reynolds number (see Table4.1). Flame B is described as transitional [46], while flames C, D, and E are all turbulent. Further, flame E presents localized extinction in the jet near-field [71]. The main jet is composed of a mixture of CH4and air, re- spectively25%and75%by volume. The equivalence ratio of the main jet is above the burning limit. A pilot flame is used to anchor the main jet to the burner exit.
The pilot is composed of a lean mixture of C2H2, H2, air, CO2, and N2, whose burnt products are the same as those of a methane/air flame atφ=0.77.
Mass fraction measurements used in this work include O2, CH4, CO, CO2, H2O, and H2 for flames B through E, which are provided by Barlowet al. [46, 71, 72].
Table4.2shows the estimated uncertainties for the measured species [46]. NO is not considered in the present work, as the steady state flamelet model (see Sec.4.3.2) is not well suited to represent slow processes such as NOxevolution [67]. The radical
4.2. Review of experimental data 50 OH is not considered due to its high sensitivity on the choice of the chemistry model.
It should be noted that for some species, signal interferences may be significant. For example, as discussed in [123] and in the proceedings of the TNF Workshop [72], the Raman scattering measurements of CH4 also include contributions from other hydrocarbon species, such that the CH4mass fraction approximates the total hydro- carbon mass fraction.
Barlow et al. [71] defined a measured mixture fraction, hereby denoted as ZTNF, and given by
ZTNF= 2YCW−YC,2
C +YH2W−YHH,2 2YC,1W−YC,2
C +YH,12W−YHH,2. (4.1) In Eq. (4.1),YCandYHare the experimentally-measured mean carbon and hydrogen mass fractions, respectively, andWC andWH are the molecular weights of carbon and hydrogen, respectively. The fuel stream has the label “2”, and the oxidizer stream has the subscript “1”. The measured mixture fraction, “ZTNF”, represents an approximation of Bilger’s definition of mixture fraction [71,128].
-0.02 0 0.02 0.04 0.06 0.08
0 0.2 0.4 0.6 0.8 1
∆Z
Z
ZTNF ZiTNF
Figure 4.1: Comparison of mixture fraction definitions computed using the optimal flamelet (see Sec. 4.3) corresponding to flame C at x/d=30. ∆Z is the difference be- tween Peters’ definition of the mixture fraction and ZTNF, computed using (i) only the measured species (solid line) and (ii) the measured species with YCH4 computed using Eq. (4.2) (dashed line). The vertical dashed line represents the stoichiometric mixture frac- tion (Zst =0.351).
4.2. Review of experimental data 51
Flame Rejet† Ujet Upilot Ucoflow [m/s] [m/s] [m/s]
B 8200 18.2 6.8 0.9
C 13400 29.7 6.8 0.9
D 22400 49.6 11.4 0.9
E 33600 74.4 17.1 0.9
Table 4.1:Flow parameters for the SANDIA flames used in this work. Data obtained from Table 1 in [46].
Scalar Systematic Scalar Systematic uncertainty uncertainty used
YO2 0.004 YH2 6-12 %
YCH4 0.005 YCO2 4 %
YH2O 4 % YCO 10-20 %
not used
YN2 3 % YNO 10-20 %
YOH 10 %
Table 4.2:Estimated systematic uncertainties for the experimentally-measured species [46, 71,123]. The uncertainties for YO2and YCH4are absolute values.
To take into account the interferences in the CH4signal, a modified form of Eq. (4.1) is considered, where the CH4mass fraction is computed as
YCHi
4 =YCH4 +YC2H2 +YC2H4 +YC2H6. (4.2) In Eq. (4.2), the “i” stands for ”interference”, and it is expected thatYCHi
4 approx- imates the total hydrocarbon mass fraction [123]. The measured mixture fraction computed using Eq. (4.2) is referred in this section as “ZiTNF”.
Multiple definitions of the mixture fraction exist in the literature. In the present work, the definition of Peters is used (see Ch. 2). A comparison of Z, ZTNF and ZiTNF is shown in Fig.4.1 for the optimal flamelet (see Sec.4.3) corresponding to flame C at x/d=30. As can be seen, due to the missing contributions of species that are not directly measured (mainly C2H2, C2H4, and C2H6), ZTNFdeviates from Z mostly on the rich side of the mixture. The analysis presented in the following sections considers the mean species mass fraction measurements conditioned on ZiTNF,hYi|ZiTNFi. Henceforth, the superscript “i” is dropped for simplicity.
†Rejetis defined asUjetd/ν, whered is the fuel pipe’s inner diameter, andνis the kinematic viscosity.